In simple terms, we define our feature learning as a mapping function \(f: {V} \rightarrow \mathbb {R}^d\)  that map all nodes(\({V}\) ) from all layers of networks \(MG_1,MG_2, \ldots MG_{L}\)  to a d-dimensional feature space, where \(d < |{V}|\) , which can be used for prediction or forecasting tasks. For each node(\(u\) ) in the given multiplex network \(MG\) , where \(u \in {V}\) , we define its multi-layer network neighborhood(\(C_u\) ). We aim to optimize the objective function, similar to the one given in [1]}, [2]}, that maximizes the following log-likelihood for neighborhood \(C_u\)  of a node u across all layers in the multiplex network as given in Equation  REF
\(\begin{aligned}& \underset{\textit {f}}{\text{\textit {max}}}& & \sum _{i \in {L}}^{} \sum _{u \in i}^{} log Pr \big ( \big (C_u\big ) | f\big (u\big ) \big )\end{aligned}\) 
